The biggest thing, to me, is how the book is organized. It looks like it will be easier than ever to find the exact rule you’re looking for when you need to know it. The first 30 or so pages offer a very organic explanation of the game’s rules, with plenty of gameplay examples for the inexperienced. It uses clear, simplified language to keep from scaring off the newcomers.
Next we have the Classes. Each class has four subclasses now. A lot of these are ones that initially appeared in other splatbooks, and they picked some good ones to port over to the PHB.
I’m a huge fan of Bards, and this PHB doesn’t disappoint. It includes my favorite Bard subclass, the “College of Glamour,” which previously appeared in Xanathar’s. It also includes the “College of Dance,” a subclass that makes Bards play a little bit like Monks. I definitely want to try that one sometime.
Speaking of Monks, I was pleased to see the “Warrior of Mercy” subclass, which previously appeared in Tasha’s Cauldron. I like this subclass because it allows you to heal your allies by punching them in the face. Okay, maybe not exactly, but you can provide healing touches as part of your Flurry of Blows, which is pretty funny.
I’m always a fan of giving healing options to non-healing classes that way. I was disappointed that they didn’t include the “Divine Soul” Sorcerer (Xanathar's), which gives Sorcerers access to Cleric spells. That’s one I’ve always wanted to try. I mean, I suppose I still can – old splatbooks are still mostly compatible - but it would have been handy to have all my favorites in one book.
Next we have Backgrounds. These are more important than ever, since these are where you get your stat bonuses. Each background lists three stats, and you have the option of picking two (+2 to one, +1 to the other), or +1 to all three. Each background also gives you a feat, skill and tool proficiencies, and equipment (or just gold if you like to buy it yourself). Despite the extra importance of these backgrounds, they actually take up less space than they did in the original PHB, with two on each page. They no longer give you roleplay bonuses like “you can always find a place to stay in an unfamiliar town,” but honestly I never saw anyone use those anyway.
Then we have Species. These also take up less space than before. The biggest change here is that there are no longer any half species. Instead, we get Aasimar, Goliath, and full-blood Orc in the PHB. If you still want to play a Half-Elf or Half-Orc, you would probably just build an Elf or an Orc and use a background appropriate to your upbringing.
Some will freak out at the fact that Races are now called Species, but then, some people freak out when they see a female Jedi, so apparently some people just need to get out more.
Then we have Feats. These are also more organized than before. The feats section is divided into Origin Feats (which you get from your background), General Feats (the ones you’re used to), Fighting Style Feats (like Duelist or Two-Weapon fighter, which used to be in the Class sections for those classes), and Epic Boon Feats (the level 20+ feats which used to be in the DM guide). This makes it much easier to find the feat you’re looking for, IMO.
Next is Equipment. Not much has changed here except for the Weapon Mastery options. If you’re playing a class that has the Weapon Mastery feature, then a lot of weapons do extra things they didn’t do before, such as cleave. In a way it makes fighters feel more like they did in 4e, which might not be a plus for everyone, but I’ll wait until I see how it plays before I pass judgement. It's a great way to give martial classes a few more options, but I'm a little worried it might undermine the simplicity I've always loved about 5e.
Next up is Spells, which as usual takes up nearly half the book. I have not gone through and read all the spells yet. I panicked a little at first when I saw that Bards have to prepare spells now. There’s reasons I prefer Bards and Sorcerers over Wizards, and one of those reasons is that their spell system is slightly less complicated. However, nothing has actually changed here except the terminology. All spellcasters “prepare spells” now. It just that Wizards prepare them every long rest, and Bards/Sorcerers prepare them whenever they gain a level. The system is the same, but the language is applied more universally.
Then there’s a small section on the Multiverse that honestly I think should have been in the DM’s guide.
Next there’s a section of Creature Stats – similar to the original PHB, it’s mostly creatures a PC might summon, ride, or transform into. It’s always nice that they do this, as it keeps non-DMs from having to buy a monster manual.
And finally we have the Rules Glossary, a place where you can quickly look up any rule or term in the game. Honestly the way this section is organized is fantastic, even if parts of it are redundant with the “how to play” section earlier in the book.
As far as Player’s Handbooks go, this version is top-notch. It excels as a guide to teach new players how to play, and it excels at helping experienced players find specific rules more easily.
